Clashes between rival militias in southern Libya have killed 20 people, a doctor at a regional hospital said, highlighting the challenge the government faces in imposing its authority months after the overthrow of Muammar Gaddafi.

A local doctor, Ibrahim Misbah, said on Monday that 20 fighters died of gunshot wounds and more than 40 people were wounded.

Local council member Ahmed Abdelkadir said clashes first broke out on Sunday between former rebel fighters from Sabha, Libya's fourth largest city, and gunmen from the Tibu tribe after a Sabha man was killed in a dispute over a car.

He said the militias opened fire at each other on the outskirts of Sabha.

"The numbers are from the Sabha side only. The Tibu wounded are being taken to a different hospital," Misbah said by phone.

Sabha fighter Oweidat al-Hifnawi said the fighting centered around the airport road and that at one point Tibu fighters controlled the entrance of the airport.

"The airport is now under our control but it is not functioning at the moment," Hifnawi said.

A witness added that the tail of an airplane on the tarmac was hit in the fighting.

It was not immediately possible to reach the Tibu side.

Asserting power

The clashes come as the ruling National Transitional Council (NTC) struggles to assert its authority across Libya, where rival militias and tribal groups are jostling for power and resources following the fall of Gaddafi.

"The situation is very dangerous and sensitive. We are following the situation and the army chief is working on sending a defence team to Sabha," deputy interior minister Omar al-Khadrawi told Libyan television.

The NTC is hampered by the lack of a coherent national army and has struggled to persuade the myriad militias who fought Gaddafi to put down their guns and join the armed forces and police.

Mustafa Abdul-Jalil, NTC chief, agreed on Monday with critics that his government is not providing strong enough leadership.

"I am not satisfied with the performance of the government or the NTC, because it is too slow in making decisions and is weak and lacks confidence in its decision making," Abdul-Jalil told The Associated Press news agency during a visit to the eastern city of Benghazi.

Last month dozens of people were killed in days of clashes between tribes in the far southeastern province of Al Kufra.

Government security forces eventually intervened to stop the fighting in a rare example of the Tripoli bureaucracy imposing its authority.

Abdul-Jalil said incompetent ministers may be dismissed in the coming months, but he gave no specifics.

A 200-member assembly to be elected in June has the job of appointing new cabinet ministers.